For the utility function, U=10X0.6Y0.4 and where the price of good X = 10, price of good Y = 20 and consumer’s income is 200, The utility level is 77.33. Please answer the following
a) Graph the indifference curve for the consumer. your graph needs to be accurate and to scale, the solution for equilibrium will be by reading values from your graphs.
b) On the same graph as above, graph the budget line and write the equation for the budget line
c) On the graph identify and optimal level on consumption of each good.
d) Calculate and show your work for marginal rate of substitution based on the answers obtained from question c. Show MRS in terms of X and Y.
e) What is market rate of substitution for the budget line
2) For the production function, U=50K0.7L0.3 and where the wage rate = 10 and capital rental rate = 20 . The desired output quantity is 440.96. Please answer the following
a) Graph the isoquant curve for the firm. your graph needs to be accurate and to scale, the solution for equilibrium will be by reading values from your graphs.
b) On the same graph as above, graph the isocost line and write the equation for it and determine the total cost of production.
c) On the graph identify the optimal level capital and labor to be used.
d) Determine marginal product of labor based on answer in c.
e) Determine the marginal product of capital based on the answer from c
f) Calculate and show your work for marginal rate of technical substitution based on the answers obtained from question c. Derive an equation for the MRTS in terms of K and L.
NOTE: for both questions, your graph needs to be accurate and to scale, the solution for equilibrium will be by reading values from your graphs.
